Classical mechanics is invariant under translations in time - this results in conservation of energy via Noether's Theorem. Classical mechanics is *not* invariant under time reversal, as others have pointed out, since this violates the Second Law of Thermodynamics. I don't know what the implications of this are via Noether's Theorem, and I would be very interested in what others more knowledgeable than myself have to say. Note also that even Quantum Field Theory is not invariant under time reversal (T), but only under the combination of CPT (C = charge conjugation and P = parity). Rowan. Henry Baker wrote:
My original question regarded "classical" GR, where interchanging "positive" and "negative" time doesn't change any laws. I.e., if you take a GR movie and simply run it backwards, it still agrees with all the GR laws.
So, you don't need any notion of "white holes" -- I'm still talking about regular old "black" holes.
So, nothing in these laws keeps such a black hole from burping an object out into space.
We can ask what initial conditions would enable such a burp & may complain that they are highly unlikely, but they aren't ruled out by the laws themselves.
Now I'm curious about what this implies for the "classical" energy, momentum, etc., of the object being burped.
At 03:40 PM 7/24/2009, Dan Asimov wrote:
Re time reversal:
The fact that in our neighborhood in spacetime we see stars radiating only in positive time -- and all the entropic consequences of this -- is usually attributed to initial conditions, not to any actual "law" of physics.
(The Ehrenfest urn model is usually considered a good microcosm of thermodynamics, and shows time reversal symmetry.)
It's just a guess, but it seems likely to me that we are aware of only a small or infinitesimal fraction of the universe, and that some other time and place have stars radiating in negative time.
(Or is it possible that entropically opposite parts of the universe somehow always end up pinching off from each other by black holes?)
--Dan
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